Manipur Board Class 12 History Question Paper 2019 with Answer Key (March 12)

BSEM Questions

• 1.

  A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height \(h\). At a point on the plane, the angle of elevation of the bottom of the flagstaff is \(\alpha\) and that of the top of the flagstaff is \(\beta\). Prove that the height of the tower is \(\dfrac{h\tan\alpha}{\tan\beta-\tan\alpha}\).

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• 2.

  Find the area of a circle whose radius is 7 cm.

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• 3.

  Find the area of the quadrilateral whose vertices are \( (1,1) \), \( (3,4) \), \( (5,-2) \) and \( (4,-7) \) taken in order.

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• 4.

  A metallic sphere of radius \(9\) cm is melted and recast to form a cylinder of radius \(3\) cm. Find the curved surface area of the cylinder.

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• 5.

  If \( \cos A = \dfrac{3}{5} \), calculate \( \sin A \) and \( \tan A \).

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• 6.

  The ratio of incomes of two persons is \(9:7\) and the ratio of their expenditures is \(4:3\). If each of them saves Rs. \(5000\) per month, find their monthly incomes.

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